Unit 1

Introduction to Computational Fluid Dynamics and Principles of Conservation: Continuity Equation, Navier Stokes Equation, Energy Equation and General Structure of Conservation Equations, Classification of Partial Differential Equations and Physical Behaviour, Approximate Solutions of Differential Equations: Error Minimization Principles.

Fundamentals of Discretization: Finite Element Method, Finite Difference and Finite Volume Method, Consistency, Stability and Convergence. 1-D Steady State Diffusion Problems- Source term linearization, Implementation of boundary conditions

Unit 2

1-D unsteady state diffusion problems: implicit, fully explicit and Crank-Nicholson scheme. Finite volume discretization of convection-diffusion problem.

Central difference scheme, Upwind scheme, Exponential scheme and Hybrid scheme, Power law scheme, Generalized convection-diffusion formulation, Finite volume discretization of two-dimensional convection-diffusion problem. The concept of false diffusion, QUICK scheme, TVD schemes and flux limiter functions.

Unit 3

Finite Volume Discretization of 2-D unsteady State Diffusion type Problems, Solution of Systems of Linear Algebraic Equations: Elimination Methods, Iterative Methods
Discretization of Navier Stokes Equations, primitive variable approach, SIMPLE Algorithm, SIMPLER Algorithm, Unstructured Grid Formulation.
Introduction to Turbulence Modeling, Important features of turbulent flow, General Properties of turbulent quantities, Reynolds average Navier stokes (RANS) equation, Closure problem in turbulence: Necessity of turbulence modeling and applications.
Laboratory practice

Course Objectives

• To study the basic governing equations and understand the basic properties of CFD.
• To understand discretization techniques and solving methods for improving accuracy.
• To inculcate the knowledge required to solve real time physical problems using simulation software.

Course Outcomes

• CO1: Understand the classification of PDEs, governing equations
• CO2: Understand the basic principles of computational methods
• CO3: Apply finite volume method to solve steady and unsteady diffusion, advection-diffusion problems
• CO4: Understand Solution algorithms and various discretization schemes.
• CO5: Solve engineering problems using CFD software

CO – PO Mapping

Textbook(s)

• Versteeg, H.K., and Malalasekara, W, “An Introduction to Computational Fluid Dynamics”, The Finite Volume Method, 2007.
• Moukalled, F., Mangani, L., &Darwish, M. “The finite volume method in computational fluid dynamics. An Advanced Introduction with OpenFOAM and Matlab”, 2016.

Reference(s)

• Patankar, S.V., “Numerical Heat Transfer and Fluid Flow”, Hemisphere Publishing Corporation, 1980.
• Anderson, J. D., & Wendt, J., “Computational fluid dynamics” (Vol. 206). New York: McGraw-Hill, 1995.

Evaluation Pattern